🎯 What is a model?
🎯 What makes a model “good”?
🎯 What is the process of modelling?
🎯 What types of models are there?
\[ y(t) = ke^{rt} \]
\[ Y = \beta_1X + \beta_0 \]
What do all of these things have in common?
\[ y(t) = ke^{rt} \]
\[ Y = \beta_1X + \beta_0 \]
All models are wrong, but some are useful.
– George E. P. Box (statistician, mid-1900s)
All models are wrong, but some are useful.
– George E. P. Box (statistician, mid-1900s)
Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful.
How much error can you tolerate in your model? Still depends on purpose!
Also, which resources do you have at your disposal?
Suppose all I have at my disposal is this campus map:
I know it takes me 10 minutes to walk from my old office to the parking lot N.
Visually estimating the relative distances, I guess it would take me 5 minutes to walk to JHE.
Suppose I now have more time and/or resources and I’m able to get (most of) the path I’d usually take measured:
distance = 350 m
average walk speed of an adult = 5 km/h or about 83 m/min
time = distance / speed
estimated time from HH to JHE: 4.2 min or 4 min, 12 seconds
Suppose I now have more time and/or resources and I’m able to get (most of) the path I’d usually take measured:
Note: just because we can get a level of precision of 4 mins and 12 seconds out of our model, doesn’t mean we should confuse this for accuracy! There are several uncertainties that can affect our estimate… Can you name some?
Suppose I now have more time and/or resources and I’m able to get (most of) the path I’d usually take measured:
May not know the size of errors induced by assumptions under uncertainty, but can at last think about potential effects on estimates (e.g. increase or decrease walking time).
Modeling is mapping between the real world and a mathematical and/or statistical framework
It’s an iterative process, and the final mapping depends on the acceptable level of error.
\[ y(t) = ke^{rt} \]
\[ Y = \beta_1X + \beta_0 \]
How could we split these models into two different groups?
mechanistic (rule-based): \[ y(t) = ke^{rt} \]
phenomenological (descriptive):
\[ Y = \beta_1X + \beta_0 \]
\[ Y = \beta_1X + \beta_0 \]
\[ Y = \beta_1X + \beta_0 \]
\[ y(t) = ke^{rt} \]
🎯 What is a model?
🎯 What makes a model “good”?
🎯 What is the process of modelling?
🎯 What types of models are there?